Heat exchanger pass effects: for the same exchanger size, tube count, and total liquid flow, the average velocity inside the tubes of a 1–4 exchanger is how many times that of a 1–1 exchanger?

Introduction / Context:
Changing the number of tube passes alters flow area per pass and thus the internal velocity for a fixed total flow. This is central to predicting Reynolds number, pressure drop, and heat-transfer coefficients when choosing heat exchanger configurations.

Given Data / Assumptions:

• Same shell and tube bundle size and same total tube count.
• Same total liquid flow rate on the tube side.
• Comparison between 1–1 and 1–4 (one shell pass, four tube passes).

Concept / Approach:
The flow area in the tubes is divided among the number of parallel flow paths operating simultaneously. A 1–4 exchanger splits the tubes into four passes; the effective cross-section per pass is one-quarter of that in 1–1. For incompressible flow at the same total rate, velocity is inversely proportional to flow area per pass.

Step-by-Step Solution:
Let A be the total tube inside area in a single-pass arrangement.In a 1–4 exchanger, area per active pass = A/4.For the same overall volumetric flow, velocity increases by factor = A/(A/4) = 4.

Verification / Alternative check:
Reynolds number scales linearly with velocity; designers use additional passes to boost h at the expense of higher pressure drop—consistent with the factor of 4.

Why Other Options Are Wrong:
(a) understates the effect; (b) and (d) invert the relation; (e) is incorrect because a clear geometric relation exists.

Common Pitfalls:
Ignoring that unequal pass counts require pass partitioning of tubes; neglecting viscosity change with temperature affecting Re and h.

Final Answer:
4